For the system of differential equations having the form(?)=P(y)

(?)=Q(x

y) (1)R.M.cooper has given in [1] an analytic Criterion for the existence of limitcycle.And a counterexample was given by Wu kiuguang in [2] to show thatcooper’s theorem is not true

He has given some additional conditions to ensurethe existence of limit cycle for system (1)

In this paper

some other sufficientconditions on existence of limit cycle for the same system (1) were obtained;besides we show that the additional conditions given by Wu kiuguang can beweakened.Our result generalize the corresponding theorems in [3].